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   <p data-fill-with="logo"><a class="logo" href="https://www.w3.org/"> <img alt="W3C" height="48" src="https://www.w3.org/StyleSheets/TR/2016/logos/W3C" width="72"> </a> </p>
   <h1 class="p-name no-ref" id="title">CSS Easing Functions Level 1</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Editor’s Draft, <time class="dt-updated" datetime="1970-01-01">1 January 1970</time></span></h2>
   <details>
    <summary>Specification Metadata</summary>
    <div data-fill-with="spec-metadata">
     <dl>
      <dt>This version:
      <dd><a class="u-url" href="https://drafts.csswg.org/css-easing/">https://drafts.csswg.org/css-easing/</a>
      <dt>Latest published version:
      <dd><a href="https://www.w3.org/TR/css-easing-1/">https://www.w3.org/TR/css-easing-1/</a>
      <dt>Previous Versions:
      <dd><a href="https://www.w3.org/TR/2018/WD-css-easing-1-20181009/" rel="prev">https://www.w3.org/TR/2018/WD-css-easing-1-20181009/</a>
      <dd><a href="https://www.w3.org/TR/2018/WD-css-timing-1-20180926/" rel="prev">https://www.w3.org/TR/2018/WD-css-timing-1-20180926/</a>
      <dd><a href="https://www.w3.org/TR/2017/WD-css-timing-1-20170221/" rel="prev">https://www.w3.org/TR/2017/WD-css-timing-1-20170221/</a>
      <dt class="editor">Editors:
      <dd class="editor p-author h-card vcard" data-editor-id="43194"><a class="p-name fn u-email email" href="mailto:bbirtles@mozilla.com">Brian Birtles</a> (<a class="p-org org" href="https://www.mozilla.org/">Mozilla</a>)
      <dd class="editor p-author h-card vcard" data-editor-id="42080"><a class="p-name fn u-email email" href="mailto:dino@apple.com">Dean Jackson</a> (<a class="p-org org" href="https://www.apple.com/">Apple Inc</a>)
      <dd class="editor p-author h-card vcard" data-editor-id="62267"><span class="p-name fn">Matt Rakow</span> (<span class="p-org org">Microsoft</span>)
      <dt class="editor">Former Editors:
      <dd class="editor p-author h-card vcard" data-editor-id="47691"><a class="p-name fn u-email email" href="mailto:shans@google.com">Shane Stephens</a> (<span class="p-org org">Google Inc</span>)
      <dd class="editor p-author h-card vcard"><span class="p-name fn"></span>
      <dt>Suggest an Edit for this Spec:
      <dd><a href="https://github.com/w3c/csswg-drafts/blob/master/css-easing-1/Overview.bs">GitHub Editor</a>
      <dt>Issue Tracking:
      <dd><a href="https://github.com/w3c/csswg-drafts/labels/css-easing-1">GitHub Issues</a>
      <dt>Participate:
      <dd>IRC: <a href="ircs://irc.w3.org:6667/css">#css</a> on W3C’s IRC
      <dt>Tests:
      <dd><a href="https://github.com/web-platform-tests/wpt/tree/master/css/css-easing">web-platform-tests css/css-easing</a>
     </dl>
    </div>
   </details>
   <div data-fill-with="warning"></div>
   <p class="copyright" data-fill-with="copyright"><a href="https://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> © 1970 <a href="https://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup> (<a href="https://www.csail.mit.edu/"><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>, <a href="https://www.ercim.eu/"><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>, <a href="https://www.keio.ac.jp/">Keio</a>, <a href="https://ev.buaa.edu.cn/">Beihang</a>). W3C <a href="https://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="https://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and <a href="https://www.w3.org/Consortium/Legal/2015/copyright-software-and-document">permissive document license</a> rules apply. </p>
   <hr title="Separator for header">
  </div>
  <div class="p-summary" data-fill-with="abstract">
   <h2 class="no-num no-toc no-ref heading settled" id="abstract"><span class="content">Abstract</span></h2>
   <p>This CSS module describes a way for authors to define a transformation

    that controls the rate of change of some value.
    Applied to animations, such transformations can be used to produce
    animations that mimic physical phenomena such as momentum or to cause the
    animation to move in discrete steps producing robot-like movement.</p>
    <a href="https://www.w3.org/TR/CSS/">CSS</a> is a language for describing the rendering of structured documents
(such as HTML and XML)
on screen, on paper, etc. 
  </div>
  <h2 class="no-num no-toc no-ref heading settled" id="status"><span class="content">Status of this document</span></h2>
  <div data-fill-with="status">
   <p> This is a public copy of the editors’ draft.
	It is provided for discussion only and may change at any moment.
	Its publication here does not imply endorsement of its contents by W3C.
	Don’t cite this document other than as work in progress. </p>
   <p> <a href="https://github.com/w3c/csswg-drafts/issues">GitHub Issues</a> are preferred for discussion of this specification.
	When filing an issue, please put the text “css-easing” in the title,
	preferably like this:
	“[css-easing] <i data-lt>…summary of comment…</i>”.
	All issues and comments are <a href="https://lists.w3.org/Archives/Public/public-css-archive/">archived</a>,
	and there is also a <a href="https://lists.w3.org/Archives/Public/www-style/">historical archive</a>. </p>
   <p> This document was produced by the <a href="https://www.w3.org/Style/CSS/">CSS Working Group</a>. </p>
   <p> This document was produced by a group operating under
	the <a href="https://www.w3.org/Consortium/Patent-Policy/">W3C Patent Policy</a>.
	W3C maintains a <a href="https://www.w3.org/2004/01/pp-impl/32061/status" rel="disclosure">public list of any patent disclosures</a> made in connection with the deliverables of the group;
	that page also includes instructions for disclosing a patent.
	An individual who has actual knowledge of a patent which the individual believes contains <a href="https://www.w3.org/Consortium/Patent-Policy/#def-essential">Essential Claim(s)</a> must disclose the information in accordance with <a href="https://www.w3.org/Consortium/Patent-Policy/#sec-Disclosure">section 6 of the W3C Patent Policy</a>. </p>
   <p> This document is governed by the <a href="https://www.w3.org/2019/Process-20190301/" id="w3c_process_revision">1 March 2019 W3C Process Document</a>. </p>
   <p></p>
  </div>
  <div data-fill-with="at-risk"></div>
  <nav data-fill-with="table-of-contents" id="toc">
   <h2 class="no-num no-toc no-ref" id="contents">Table of Contents</h2>
   <ol class="toc" role="directory">
    <li><a href="#introduction"><span class="secno">1</span> <span class="content">Introduction</span></a>
    <li>
     <a href="#easing-functions"><span class="secno">2</span> <span class="content">Easing functions</span></a>
     <ol class="toc">
      <li><a href="#the-linear-easing-function"><span class="secno">2.1</span> <span class="content">The linear easing function: <span class="css">linear</span></span></a>
      <li>
       <a href="#cubic-bezier-easing-functions"><span class="secno">2.2</span> <span class="content">Cubic
Bézier easing functions: <span class="css">ease</span>, <span class="css">ease-in</span>, <span class="css">ease-out</span>, <span class="css">ease-in-out</span>, <span class="css">cubic-bezier()</span></span></a>
       <ol class="toc">
        <li><a href="#cubic-bezier-algo"><span class="secno">2.2.1</span> <span class="content">Output of a cubic bézier easing function</span></a>
       </ol>
      <li>
       <a href="#step-easing-functions"><span class="secno">2.3</span> <span class="content">Step easing functions: <span class="css">step-start</span>, <span class="css">step-end</span>, <span class="css">steps()</span></span></a>
       <ol class="toc">
        <li><a href="#step-easing-algo"><span class="secno">2.3.1</span> <span class="content">Output of
a step easing function</span></a>
       </ol>
      <li><a href="#serialization"><span class="secno">2.4</span> <span class="content">Serialization</span></a>
     </ol>
    <li><a href="#priv-sec"><span class="secno">3</span> <span class="content">Privacy and Security Considerations</span></a>
    <li><a href="#changes"><span class="secno">4</span> <span class="content">Changes since last publication</span></a>
    <li><a href="#acknowledgements"><span class="secno">5</span> <span class="content">Acknowledgements</span></a>
    <li>
     <a href="#conformance"><span class="secno"></span> <span class="content"> Conformance</span></a>
     <ol class="toc">
      <li><a href="#document-conventions"><span class="secno"></span> <span class="content"> Document conventions</span></a>
      <li><a href="#conform-classes"><span class="secno"></span> <span class="content"> Conformance classes</span></a>
      <li>
       <a href="#conform-responsible"><span class="secno"></span> <span class="content"> Requirements for Responsible Implementation of CSS</span></a>
       <ol class="toc">
        <li><a href="#conform-partial"><span class="secno"></span> <span class="content"> Partial Implementations</span></a>
        <li><a href="#conform-future-proofing"><span class="secno"></span> <span class="content"> Implementations of Unstable and Proprietary Features</span></a>
        <li><a href="#conform-testing"><span class="secno"></span> <span class="content"> Implementations of CR-level Features</span></a>
       </ol>
     </ol>
    <li>
     <a href="#index"><span class="secno"></span> <span class="content">Index</span></a>
     <ol class="toc">
      <li><a href="#index-defined-here"><span class="secno"></span> <span class="content">Terms defined by this specification</span></a>
      <li><a href="#index-defined-elsewhere"><span class="secno"></span> <span class="content">Terms defined by reference</span></a>
     </ol>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#normative"><span class="secno"></span> <span class="content">Normative References</span></a>
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <h2 class="heading settled" data-level="1" id="introduction"><span class="secno">1. </span><span class="content">Introduction</span><a class="self-link" href="#introduction"></a></h2>
   <p><em>This section is not normative.</em></p>
   <p>It is often desirable to control the rate at which some value changes.
For example, gradually increasing the speed at which an element moves can
give the element a sense of weight as it appears to gather momentum.
This can be used to produce intuitive user interface elements or convincing
cartoon props that behave like their physical counterparts.
Alternatively, it is sometimes desirable for animation to move forwards in
distinct steps such as a segmented wheel that rotates such that the segments
always appear in the same position.</p>
   <p>Similarly, controlling the rate of change of gradient interpolation can be
used to produce different visual effects such as suggesting a concave or convex
surface, or producing a striped effect.</p>
   <p><a data-link-type="dfn" href="#easing-function" id="ref-for-easing-function">Easing functions</a> provide a means to transform such values by taking an
input progress value and producing a corresponding transformed output progress
value.</p>
   <figure>
     <img alt="Example of an easing function that produces an ease-in effect." src="easing-function-example.svg" width="400"> 
    <figcaption> Example of an easing function that produces an ease-in effect.<br> Given an input progress of 0.7, the easing function scales the
    value to produce an output progress of 0.52.<br> Applying this easing function to an animation would cause it to progress
    more slowly at first but then gradually progress more quickly. </figcaption>
   </figure>
   <h2 class="heading settled" data-level="2" id="easing-functions"><span class="secno">2. </span><span class="content">Easing functions</span><span id="timing-functions"></span><a class="self-link" href="#easing-functions"></a></h2>
   <p>An <dfn class="dfn-paneled" data-dfn-type="dfn" data-export data-lt="easing function|timing function" id="easing-function">easing function</dfn> takes
an <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value">input progress value</a> and produces an <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value">output progress value</a>.</p>
   <p>An <a data-link-type="dfn" href="#easing-function" id="ref-for-easing-function①">easing function</a> must be a pure function meaning that for a given set of
inputs, it always produces the same <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value①">output progress value</a>.</p>
   <p>The <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="input-progress-value">input progress value</dfn> is a real number in the range [-∞,
∞].
Typically, the <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①">input progress value</a> is in the range [0, 1] but this may
not be the case when <a data-link-type="dfn" href="#easing-function" id="ref-for-easing-function②">easing functions</a> are chained together.</p>
   <p>The <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="output-progress-value">output progress value</dfn> is a real number in the
range [-∞, ∞].</p>
   <p>Some types of easing functions also take an additional boolean <a data-link-type="dfn" href="#before-flag" id="ref-for-before-flag">before flag</a> input which is defined subsequently.</p>
   <p>This specification defines four types of easing functions whose definitions
follow.</p>
   <p>The syntax for specifying an <a data-link-type="dfn" href="#easing-function" id="ref-for-easing-function③">easing function</a> is as follows:</p>
   <div class="prod"><dfn class="css" data-dfn-type="type" data-export id="typedef-easing-function">&lt;easing-function><a class="self-link" href="#typedef-easing-function"></a></dfn> = <a class="css" data-link-type="maybe" href="#valdef-easing-function-linear" id="ref-for-valdef-easing-function-linear">linear</a> <a data-link-type="grammar" href="https://drafts.csswg.org/css-values-4/#comb-one" id="ref-for-comb-one">|</a> <a class="production css" data-link-type="type" href="#typedef-cubic-bezier-easing-function" id="ref-for-typedef-cubic-bezier-easing-function" title="Expands to: ease-in-out | cubic-bezier() | ease | ease-in | ease-out">&lt;cubic-bezier-easing-function></a> <span id="ref-for-comb-one①">|</span> <a class="production css" data-link-type="type" href="#typedef-step-easing-function" id="ref-for-typedef-step-easing-function" title="Expands to: steps() | step-end | step-start">&lt;step-easing-function></a></div>
   <h3 class="heading settled" data-level="2.1" id="the-linear-easing-function"><span class="secno">2.1. </span><span class="content">The linear easing function: <a class="css" data-link-type="maybe" href="#valdef-easing-function-linear" id="ref-for-valdef-easing-function-linear①">linear</a></span><span id="linear-timing-function-section"></span><a class="self-link" href="#the-linear-easing-function"></a></h3>
   <p>The <dfn class="dfn-paneled" data-dfn-type="dfn" data-export data-lt="linear easing function|linear timing function" id="linear-easing-function">linear easing
function</dfn> is an identity function
meaning that its <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value②">output progress value</a> is equal to the <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value②">input progress value</a> for all inputs.</p>
   <p>The syntax for the <a data-link-type="dfn" href="#linear-easing-function" id="ref-for-linear-easing-function">linear easing function</a> is simply the <dfn class="dfn-paneled css" data-dfn-for="easing-function" data-dfn-type="value" data-export id="valdef-easing-function-linear">linear</dfn> keyword.</p>
   <h3 class="heading settled" data-level="2.2" id="cubic-bezier-easing-functions"><span class="secno">2.2. </span><span class="content">Cubic
Bézier easing functions: <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease" id="ref-for-valdef-cubic-bezier-easing-function-ease">ease</a>, <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-in" id="ref-for-valdef-cubic-bezier-easing-function-ease-in">ease-in</a>, <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-out" id="ref-for-valdef-cubic-bezier-easing-function-ease-out">ease-out</a>, <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-in-out" id="ref-for-valdef-cubic-bezier-easing-function-ease-in-out">ease-in-out</a>, <a class="css" data-link-type="maybe" href="#funcdef-cubic-bezier-easing-function-cubic-bezier" id="ref-for-funcdef-cubic-bezier-easing-function-cubic-bezier">cubic-bezier()</a></span><span id="cubic-bezier-timing-functions"></span><a class="self-link" href="#cubic-bezier-easing-functions"></a></h3>
   <p>A <dfn class="dfn-paneled" data-dfn-type="dfn" data-export id="cubic-bzier-easing-function">cubic Bézier easing function</dfn> is
a type of <a data-link-type="dfn" href="#easing-function" id="ref-for-easing-function④">easing function</a> defined by four real numbers
that specify the two control points, <var>P1</var> and <var>P2</var>, of a cubic Bézier curve whose
end points <var>P0</var> and <var>P3</var> are fixed at (0, 0) and (1, 1) respectively.
The <var>x</var> coordinates of <var>P1</var> and <var>P2</var> are restricted to the range [0, 1].</p>
   <figure>
     <img alt="A cubic Bezier curve used as an easing function." src="cubic-bezier-easing-curve.svg" width="400"> 
    <figcaption> A cubic Bézier curve used as an easing function.<br> The shape of the curve is determined by the location of the control
    points <var>P1</var> and <var>P2</var>.<br> Input progress values serve as <var>x</var> values of the curve,
    whilst the <var>y</var> values are the output progress values. </figcaption>
   </figure>
   <p>A <a data-link-type="dfn" href="#cubic-bzier-easing-function" id="ref-for-cubic-bzier-easing-function">cubic Bézier easing function</a> has the following syntax
(using notation from <a data-link-type="biblio" href="#biblio-css3val">[CSS3VAL]</a>):</p>
   <div class="prod"><dfn class="dfn-paneled css" data-dfn-type="type" data-export id="typedef-cubic-bezier-easing-function">&lt;cubic-bezier-easing-function></dfn> = <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease" id="ref-for-valdef-cubic-bezier-easing-function-ease①">ease</a> <a data-link-type="grammar" href="https://drafts.csswg.org/css-values-4/#comb-one" id="ref-for-comb-one②">|</a> <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-in" id="ref-for-valdef-cubic-bezier-easing-function-ease-in①">ease-in</a> <span id="ref-for-comb-one③">|</span> <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-out" id="ref-for-valdef-cubic-bezier-easing-function-ease-out①">ease-out</a> <span id="ref-for-comb-one④">|</span> <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-in-out" id="ref-for-valdef-cubic-bezier-easing-function-ease-in-out①">ease-in-out</a> <span id="ref-for-comb-one⑤">|</span> <span class="atom"><a class="css" data-link-type="function" href="#funcdef-cubic-bezier-easing-function-cubic-bezier" id="ref-for-funcdef-cubic-bezier-easing-function-cubic-bezier①">cubic-bezier</a>(<a class="production css" data-link-type="type" href="https://drafts.csswg.org/css-values-3/#number-value" id="ref-for-number-value">&lt;number></a><a data-link-type="grammar" href="https://drafts.csswg.org/css-values-4/#comb-comma" id="ref-for-comb-comma">,</a> <span class="production" id="ref-for-number-value①">&lt;number></span><span id="ref-for-comb-comma①">,</span> <span class="production" id="ref-for-number-value②">&lt;number></span><span id="ref-for-comb-comma②">,</span> <span class="production" id="ref-for-number-value③">&lt;number></span>)</span></div>
   <p>The meaning of each value is as follows:</p>
   <dl>
    <dt data-md><dfn class="dfn-paneled css" data-dfn-for="cubic-bezier-easing-function, <cubic-bezier-easing-function>" data-dfn-type="value" data-export id="valdef-cubic-bezier-easing-function-ease">ease</dfn>
    <dd data-md>
     <p>Equivalent to <span class="css">cubic-bezier(0.25, 0.1, 0.25, 1)</span>.</p>
    <dt data-md><dfn class="dfn-paneled css" data-dfn-for="cubic-bezier-easing-function, <cubic-bezier-easing-function>" data-dfn-type="value" data-export id="valdef-cubic-bezier-easing-function-ease-in">ease-in</dfn>
    <dd data-md>
     <p>Equivalent to <span class="css">cubic-bezier(0.42, 0, 1, 1)</span>.</p>
    <dt data-md><dfn class="dfn-paneled css" data-dfn-for="cubic-bezier-easing-function, <cubic-bezier-easing-function>" data-dfn-type="value" data-export id="valdef-cubic-bezier-easing-function-ease-out">ease-out</dfn>
    <dd data-md>
     <p>Equivalent to <span class="css">cubic-bezier(0, 0, 0.58, 1)</span>.</p>
    <dt data-md><dfn class="dfn-paneled css" data-dfn-for="cubic-bezier-easing-function, <cubic-bezier-easing-function>" data-dfn-type="value" data-export id="valdef-cubic-bezier-easing-function-ease-in-out">ease-in-out</dfn>
    <dd data-md>
     <p>Equivalent to <span class="css">cubic-bezier(0.42, 0, 0.58, 1)</span>.</p>
    <dt data-md>
    <dt><dfn class="dfn-paneled css" data-dfn-for="cubic-bezier-easing-function, <cubic-bezier-easing-function>" data-dfn-type="function" data-export data-lt="cubic-bezier()" id="funcdef-cubic-bezier-easing-function-cubic-bezier">cubic-bezier(<a class="production css" data-link-type="type" href="https://drafts.csswg.org/css-values-3/#number-value" id="ref-for-number-value④">&lt;number></a>, <span class="production" id="ref-for-number-value⑤">&lt;number></span>, <span class="production" id="ref-for-number-value⑥">&lt;number></span>, <span class="production" id="ref-for-number-value⑦">&lt;number></span>)</dfn>
    <dd data-md>
     <p>Specifies a <a data-link-type="dfn" href="#cubic-bzier-easing-function" id="ref-for-cubic-bzier-easing-function①">cubic Bézier easing function</a>.
The four numbers specify points <var>P1</var> and <var>P2</var> of
the curve as (<var>x1</var>, <var>y1</var>, <var>x2</var>, <var>y2</var>).
Both <var>x</var> values must be in the range [0, 1] or the definition is
invalid.</p>
   </dl>
   <p>The keyword values listed above are illustrated below.</p>
   <figure>
     <img alt="The easing functions produced by keyword values." src="curve-keywords.svg" width="500"> 
    <figcaption> The easing functions produced by each of the cubic Bézier easing
    function keyword values. </figcaption>
   </figure>
   <h4 class="heading settled" data-level="2.2.1" id="cubic-bezier-algo"><span class="secno">2.2.1. </span><span class="content">Output of a cubic bézier easing function</span><a class="self-link" href="#cubic-bezier-algo"></a></h4>
   <p>The mapping from input progress to output progress is performed by
determining the corresponding <var>y</var> value (<a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value③">output progress value</a>) for
a given <var>x</var> value (<a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value③">input progress value</a>).
The evaluation of this curve is covered in many sources such as <a data-link-type="biblio" href="#biblio-fund-comp-graphics">[FUND-COMP-GRAPHICS]</a>.</p>
   <p>For <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value④">input progress values</a> outside the range [0, 1], the curve is extended
infinitely using tangent of the curve at the closest endpoint as follows:</p>
   <ul>
    <li data-md>
     <p>For <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value⑤">input progress values</a> less than zero,</p>
     <ol>
      <li data-md>
       <p>If the <var>x</var> value of P1 is greater than zero, use
 a straight line that passes through P1 and P0 as the tangent.</p>
      <li data-md>
       <p>Otherwise, if the <var>x</var> value of P2 is greater than
 zero, use a straight line that passes through P2 and P0 as the tangent.</p>
      <li data-md>
       <p>Otherwise, let the <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value④">output progress value</a> be zero for all <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value⑥">input progress values</a> in the range [-∞, 0).</p>
     </ol>
    <li data-md>
     <p>For <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value⑦">input progress values</a> greater than one,</p>
     <ol>
      <li data-md>
       <p>If the <var>x</var> value of P2 is less than one, use
 a straight line that passes through P2 and P3 as the tangent.</p>
      <li data-md>
       <p>Otherwise, if the <var>x</var> value of P1 is less than
 one, use a straight line that passes through P1 and P3 as the tangent.</p>
      <li data-md>
       <p>Otherwise, let the <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value⑤">output progress value</a> be one for all <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value⑧">input progress values</a> in the range (1, ∞].</p>
     </ol>
   </ul>
   <h3 class="heading settled" data-level="2.3" id="step-easing-functions"><span class="secno">2.3. </span><span class="content">Step easing functions: <a class="css" data-link-type="maybe" href="#valdef-step-easing-function-step-start" id="ref-for-valdef-step-easing-function-step-start">step-start</a>, <a class="css" data-link-type="maybe" href="#valdef-step-easing-function-step-end" id="ref-for-valdef-step-easing-function-step-end">step-end</a>, <a class="css" data-link-type="maybe" href="#funcdef-step-easing-function-steps" id="ref-for-funcdef-step-easing-function-steps">steps()</a></span><span id="step-timing-functions"></span><a class="self-link" href="#step-easing-functions"></a></h3>
   <p>A <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="step-easing-function">step easing function</dfn> is a type of <a data-link-type="dfn" href="#easing-function" id="ref-for-easing-function⑤">easing function</a> that divides the input time into a specified number of intervals that
are equal in length.
It is defined by a number of <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="steps">steps</dfn>, and a <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="step-position">step position</dfn>.
It has following syntax:</p>
   <div class="prod">
     <dfn class="dfn-paneled css" data-dfn-type="type" data-export id="typedef-step-easing-function">&lt;step-easing-function></dfn> = <a class="css" data-link-type="maybe" href="#valdef-step-easing-function-step-start" id="ref-for-valdef-step-easing-function-step-start①">step-start</a> <a data-link-type="grammar" href="https://drafts.csswg.org/css-values-4/#comb-one" id="ref-for-comb-one⑥">|</a> <a class="css" data-link-type="maybe" href="#valdef-step-easing-function-step-end" id="ref-for-valdef-step-easing-function-step-end①">step-end</a> <span id="ref-for-comb-one⑦">|</span> <span class="atom"><a class="css" data-link-type="function" href="#funcdef-step-easing-function-steps" id="ref-for-funcdef-step-easing-function-steps①">steps</a>(<a class="production css" data-link-type="type" href="https://drafts.csswg.org/css-values-3/#integer-value" id="ref-for-integer-value">&lt;integer></a>[<a data-link-type="grammar" href="https://drafts.csswg.org/css-values-4/#comb-comma" id="ref-for-comb-comma③">,</a> <a class="production css" data-link-type="type" href="#typedef-step-position" id="ref-for-typedef-step-position">&lt;step-position></a>]<a data-link-type="grammar" href="https://drafts.csswg.org/css-values-4/#mult-opt" id="ref-for-mult-opt">?</a>)</span> 
    <p><dfn class="dfn-paneled css" data-dfn-type="type" data-export id="typedef-step-position">&lt;step-position></dfn> = <a class="css" data-link-type="maybe" href="#valdef-steps-jump-start" id="ref-for-valdef-steps-jump-start">jump-start</a> <a data-link-type="grammar" href="https://drafts.csswg.org/css-values-4/#comb-one" id="ref-for-comb-one⑧">|</a> <a class="css" data-link-type="maybe" href="#valdef-steps-jump-end" id="ref-for-valdef-steps-jump-end">jump-end</a> <span id="ref-for-comb-one⑨">|</span> <a class="css" data-link-type="maybe" href="#valdef-steps-jump-none" id="ref-for-valdef-steps-jump-none">jump-none</a> <span id="ref-for-comb-one①⓪">|</span> <a class="css" data-link-type="maybe" href="#valdef-steps-jump-both" id="ref-for-valdef-steps-jump-both">jump-both</a> <span id="ref-for-comb-one①①">|</span> <a class="css" data-link-type="maybe" href="#valdef-steps-start" id="ref-for-valdef-steps-start">start</a> <span id="ref-for-comb-one①②">|</span> <a class="css" data-link-type="maybe" href="#valdef-steps-end" id="ref-for-valdef-steps-end">end</a></p>
   </div>
   <p></p>
   <p>The meaning of each value is as follows:</p>
   <dl>
    <dt data-md><dfn class="dfn-paneled css" data-dfn-for="step-easing-function, <step-easing-function>" data-dfn-type="value" data-export id="valdef-step-easing-function-step-start">step-start</dfn>
    <dd data-md>
     <p>Computes to <span class="css">steps(1, start)</span></p>
    <dt data-md><dfn class="dfn-paneled css" data-dfn-for="step-easing-function, <step-easing-function>" data-dfn-type="value" data-export id="valdef-step-easing-function-step-end">step-end</dfn>
    <dd data-md>
     <p>Computes to <span class="css">steps(1, end)</span></p>
     <figure>
       <img alt="Example step easing keywords." src="step-easing-keyword-examples.svg" width="500"> 
      <figcaption> Example step easing function keyword values. </figcaption>
     </figure>
    <dt data-md><dfn class="dfn-paneled css" data-dfn-for="step-easing-function, <step-easing-function>" data-dfn-type="function" data-export data-lt="steps()" id="funcdef-step-easing-function-steps">steps(&lt;integer>[, &lt;step-position> ]?)</dfn>
    <dd data-md>
     <p>The first parameter specifies the number of intervals in the function.
It must be a positive integer greater than 0
unless the second parameter is <a class="css" data-link-type="value" href="#valdef-steps-jump-none" id="ref-for-valdef-steps-jump-none①">jump-none</a> in which case it must be a positive integer greater than 1.</p>
     <p>The second parameter, which is optional, specifies the <a data-link-type="dfn" href="#step-position" id="ref-for-step-position">step position</a> using one of the following values:</p>
     <dl>
      <dt data-md><dfn class="dfn-paneled css" data-dfn-for="steps()" data-dfn-type="value" data-export id="valdef-steps-jump-start">jump-start</dfn>
      <dd data-md>
       <p>The first rise occurs at <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value⑨">input progress value</a> of 0.</p>
      <dt data-md><dfn class="dfn-paneled css" data-dfn-for="steps()" data-dfn-type="value" data-export id="valdef-steps-jump-end">jump-end</dfn>
      <dd data-md>
       <p>The last rise occurs at <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①⓪">input progress value</a> of 1.</p>
      <dt data-md><dfn class="dfn-paneled css" data-dfn-for="steps()" data-dfn-type="value" data-export id="valdef-steps-jump-none">jump-none</dfn>
      <dd data-md>
       <p>All rises occur within the range (0, 1).</p>
      <dt data-md><dfn class="dfn-paneled css" data-dfn-for="steps()" data-dfn-type="value" data-export id="valdef-steps-jump-both">jump-both</dfn>
      <dd data-md>
       <p>The first rise occurs at <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①①">input progress value</a> of 0
and the last rise occurs at <span id="ref-for-input-progress-value①②">input progress value</span> of 1.</p>
      <dt data-md><dfn class="dfn-paneled css" data-dfn-for="steps()" data-dfn-type="value" data-export id="valdef-steps-start">start</dfn>
      <dd data-md>
       <p>Behaves as <a class="css" data-link-type="value" href="#valdef-steps-jump-start" id="ref-for-valdef-steps-jump-start①">jump-start</a>.</p>
      <dt data-md><dfn class="dfn-paneled css" data-dfn-for="steps()" data-dfn-type="value" data-export id="valdef-steps-end">end</dfn>
      <dd data-md>
       <p>Behaves as <a class="css" data-link-type="value" href="#valdef-steps-jump-end" id="ref-for-valdef-steps-jump-end①">jump-end</a>.</p>
     </dl>
     <p>If the second parameter is omitted, the value <a class="css" data-link-type="maybe" href="#valdef-steps-end" id="ref-for-valdef-steps-end①">end</a> is assumed.</p>
     <p>These values are illustrated below:</p>
     <figure>
       <img alt="Example step easing functions." src="step-easing-func-examples.svg" width="500"> 
      <figcaption> Example step easing functions. </figcaption>
     </figure>
   </dl>
   <h4 class="heading settled" data-level="2.3.1" id="step-easing-algo"><span class="secno">2.3.1. </span><span class="content">Output of
a step easing function</span><span id="step-timing-function-algo"></span><a class="self-link" href="#step-easing-algo"></a></h4>
   <p>At the exact point where a step occurs, the result of the function is
conceptually the top of the step. However, an additional <dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="before-flag">before flag</dfn> passed as input to the <a data-link-type="dfn" href="#step-easing-function" id="ref-for-step-easing-function">step easing function</a>, if true, will cause the
result of the function to correspond to the bottom of the step at the step
point.</p>
   <div class="example" id="example-7b6395b6">
    <a class="self-link" href="#example-7b6395b6"></a> 
    <p>As an example of how the <a data-link-type="dfn" href="#before-flag" id="ref-for-before-flag①">before flag</a> affects the behavior of this function,
consider an animation with a <a data-link-type="dfn" href="#step-easing-function" id="ref-for-step-easing-function①">step easing function</a> whose <a data-link-type="dfn" href="#step-position" id="ref-for-step-position①">step
position</a> is <a class="css" data-link-type="value" href="#valdef-steps-start" id="ref-for-valdef-steps-start①">start</a> and which has a positive
delay and backwards fill.</p>
    <p>For example, using CSS animation:</p>
<pre class="lang-css highlight">animation: moveRight 5s 1s steps(5, start);
</pre>
    <p>During the delay phase, the <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①③">input progress value</a> will be zero but if the <a data-link-type="dfn" href="#before-flag" id="ref-for-before-flag②">before flag</a> is set to indicate that the animation has yet to reach its
animation interval, the easing function will produce zero as its <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value⑥">output
progress value</a>, i.e. the bottom of the first step.</p>
    <p>At the exact moment when the animation interval begins, the <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①④">input progress
value</a> will still be zero, but the <a data-link-type="dfn" href="#before-flag" id="ref-for-before-flag③">before flag</a> will not be set and hence
the result of the easing function will correspond to the top of the first step.</p>
   </div>
   <p>For the purposes of calculating the <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value⑦">output progress value</a>, the <a data-link-type="dfn" href="#step-position" id="ref-for-step-position②">step position</a> <a class="css" data-link-type="value" href="#valdef-steps-start" id="ref-for-valdef-steps-start②">start</a> is considered equivalent to <a class="css" data-link-type="value" href="#valdef-steps-jump-start" id="ref-for-valdef-steps-jump-start②">jump-start</a>.
Likewise <a class="css" data-link-type="value" href="#valdef-steps-end" id="ref-for-valdef-steps-end②">end</a> is considered equivalent to <a class="css" data-link-type="value" href="#valdef-steps-jump-end" id="ref-for-valdef-steps-jump-end②">jump-end</a>.
As a result, the following algorithm does not make explicit reference to <span id="ref-for-valdef-steps-start③">start</span> or <span id="ref-for-valdef-steps-end③">end</span>.</p>
   <p class="note" role="note"><span>Note:</span> User agents must still differentiate between <a class="css" data-link-type="value" href="#valdef-steps-jump-start" id="ref-for-valdef-steps-jump-start③">jump-start</a> and <a class="css" data-link-type="value" href="#valdef-steps-start" id="ref-for-valdef-steps-start④">start</a> for
the purpose of serialization (see <a href="#serialization">§ 2.4 Serialization</a>).</p>
   <p>The <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value⑧">output progress value</a> is calculated from the <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①⑤">input progress value</a> and <a data-link-type="dfn" href="#before-flag" id="ref-for-before-flag④">before flag</a> as follows:</p>
   <ol>
    <li data-md>
     <p>Calculate the <var>current step</var> as <code>floor(<a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①⑥">input progress value</a> × <a data-link-type="dfn" href="#steps" id="ref-for-steps">steps</a>)</code>.</p>
    <li data-md>
     <p>If the <a data-link-type="dfn" href="#step-position" id="ref-for-step-position③">step position</a> property is one of:</p>
     <ul>
      <li data-md>
       <p><a class="css" data-link-type="value" href="#valdef-steps-jump-start" id="ref-for-valdef-steps-jump-start④">jump-start</a>,</p>
      <li data-md>
       <p><a class="css" data-link-type="value" href="#valdef-steps-jump-both" id="ref-for-valdef-steps-jump-both①">jump-both</a>,</p>
     </ul>
     <p>increment <var>current step</var> by one.</p>
    <li data-md>
     <p>If <em>both</em> of the following conditions are true:</p>
     <ul>
      <li data-md>
       <p>the <a data-link-type="dfn" href="#before-flag" id="ref-for-before-flag⑤">before flag</a> is set, <em>and</em></p>
      <li data-md>
       <p><a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①⑦">input progress value</a> × <a data-link-type="dfn" href="#steps" id="ref-for-steps①">steps</a> mod 1 equals zero
 (that is, if <span id="ref-for-input-progress-value①⑧">input progress value</span> × <span id="ref-for-steps②">steps</span> is
 integral), then</p>
     </ul>
     <p>decrement <var>current step</var> by one.</p>
    <li data-md>
     <p>If <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value①⑨">input progress value</a> ≥ 0 and <var>current step</var> &lt; 0,
 let <var>current step</var> be zero.</p>
    <li data-md>
     <p>Calculate <var>jumps</var> based on the <a data-link-type="dfn" href="#step-position" id="ref-for-step-position④">step position</a> as follows:</p>
     <dl>
      <dt data-md><a class="css" data-link-type="value" href="#valdef-steps-jump-start" id="ref-for-valdef-steps-jump-start⑤">jump-start</a> or <a class="css" data-link-type="value" href="#valdef-steps-jump-end" id="ref-for-valdef-steps-jump-end③">jump-end</a>
      <dd data-md>
       <p><a data-link-type="dfn" href="#steps" id="ref-for-steps③">steps</a></p>
      <dt data-md><a class="css" data-link-type="value" href="#valdef-steps-jump-none" id="ref-for-valdef-steps-jump-none②">jump-none</a>
      <dd data-md>
       <p><a data-link-type="dfn" href="#steps" id="ref-for-steps④">steps</a> - 1</p>
      <dt data-md><a class="css" data-link-type="value" href="#valdef-steps-jump-both" id="ref-for-valdef-steps-jump-both②">jump-both</a>
      <dd data-md>
       <p><a data-link-type="dfn" href="#steps" id="ref-for-steps⑤">steps</a> + 1</p>
     </dl>
    <li data-md>
     <p>If <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value②⓪">input progress value</a> ≤ 1 and <var>current step</var> > <var>jumps</var>, let <var>current step</var> be <var>jumps</var>.</p>
     <div class="note" role="note">
      <p>Steps 4 and 6 in this procedure ensure that given an <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value②①">input progress
 value</a> in the range [0, 1], a step easing function does not produce an <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value⑨">output progress value</a> outside that range.</p>
      <p>For example, although mathematically we might expect that a step easing
 function with a <a data-link-type="dfn" href="#step-position" id="ref-for-step-position⑤">step position</a> of <a class="css" data-link-type="value" href="#valdef-steps-jump-start" id="ref-for-valdef-steps-jump-start⑥">jump-start</a> would step up (i.e. beyond 1) when the <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value②②">input progress value</a> is 1,
 intuitively,
 when we apply such an easing function to a forwards-filling animation,
 we expect it to produce an <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value①⓪">output progress value</a> of 1
 as the animation fills forwards.</p>
      <p>A similar situation arises for a step easing function with
 a <a data-link-type="dfn" href="#step-position" id="ref-for-step-position⑥">step position</a> of <a class="css" data-link-type="value" href="#valdef-steps-jump-end" id="ref-for-valdef-steps-jump-end④">jump-end</a> when applied to an animation during its delay phase.</p>
     </div>
    <li data-md>
     <p>The <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value①①">output progress value</a> is <code><var>current step</var> / <var>jumps</var></code>.</p>
   </ol>
   <h3 class="heading settled" data-level="2.4" id="serialization"><span class="secno">2.4. </span><span class="content">Serialization</span><span id="serializing-a-timing-function"></span><a class="self-link" href="#serialization"></a></h3>
   <p>Easing functions are serialized using the common serialization patterns
defined in <a data-link-type="biblio" href="#biblio-cssom">[CSSOM]</a> with the following additional requirements:</p>
   <ul>
    <li data-md>
     <p>The keyword values <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease" id="ref-for-valdef-cubic-bezier-easing-function-ease②">ease</a>, <a class="css" data-link-type="maybe" href="#valdef-easing-function-linear" id="ref-for-valdef-easing-function-linear②">linear</a>, <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-in" id="ref-for-valdef-cubic-bezier-easing-function-ease-in②">ease-in</a>, <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-out" id="ref-for-valdef-cubic-bezier-easing-function-ease-out②">ease-out</a>,
and <a class="css" data-link-type="maybe" href="#valdef-cubic-bezier-easing-function-ease-in-out" id="ref-for-valdef-cubic-bezier-easing-function-ease-in-out②">ease-in-out</a> are serialized as-is, that is, they are <em>not</em> converted to the equivalent <a class="css" data-link-type="maybe" href="#funcdef-cubic-bezier-easing-function-cubic-bezier" id="ref-for-funcdef-cubic-bezier-easing-function-cubic-bezier②">cubic-bezier()</a> function before serializing.</p>
    <li data-md>
     <p>Step easing functions, whether they are specified using the <a class="css" data-link-type="maybe" href="#funcdef-step-easing-function-steps" id="ref-for-funcdef-step-easing-function-steps②">steps()</a> function or either of the <a class="css" data-link-type="maybe" href="#valdef-step-easing-function-step-start" id="ref-for-valdef-step-easing-function-step-start②">step-start</a> or <a class="css" data-link-type="maybe" href="#valdef-step-easing-function-step-end" id="ref-for-valdef-step-easing-function-step-end②">step-end</a> keywords, are serialized as follows:</p>
     <ol>
      <li data-md>
       <p>If the <a data-link-type="dfn" href="#step-position" id="ref-for-step-position⑦">step position</a> is <a class="css" data-link-type="maybe" href="#valdef-steps-jump-end" id="ref-for-valdef-steps-jump-end⑤">jump-end</a> or <a class="css" data-link-type="maybe" href="#valdef-steps-end" id="ref-for-valdef-steps-end④">end</a>, serialize
 as <a class="css" data-link-type="function" href="#funcdef-step-easing-function-steps" id="ref-for-funcdef-step-easing-function-steps③">steps(&lt;integer>)</a>.</p>
      <li data-md>
       <p>Otherwise, serialize as <a class="css" data-link-type="function" href="#funcdef-step-easing-function-steps" id="ref-for-funcdef-step-easing-function-steps④">steps(&lt;integer>, &lt;step-position>)</a>.</p>
     </ol>
   </ul>
   <h2 class="heading settled" data-level="3" id="priv-sec"><span class="secno">3. </span><span class="content">Privacy and Security Considerations</span><a class="self-link" href="#priv-sec"></a></h2>
   <p>This specification does not directly introduce any new capabilities to the
Web platform but rather provides common definitions that may be referenced by
other specifications.
As a result, it does not introduce any new privacy and security concerns.</p>
   <p>Specifications referencing the features defined in this specification
should consider that while easing functions most commonly
take an <a data-link-type="dfn" href="#input-progress-value" id="ref-for-input-progress-value②③">input progress value</a> in the range [0,1]
and produce an <a data-link-type="dfn" href="#output-progress-value" id="ref-for-output-progress-value①②">output progress value</a> in the range [0, 1],
this is not always the case.
Applications of easing functions should
define the behavior for inputs and outputs outside this range
to ensure they do not introduce new security considerations.</p>
   <h2 class="heading settled" data-level="4" id="changes"><span class="secno">4. </span><span class="content">Changes since last publication</span><a class="self-link" href="#changes"></a></h2>
   <p>The following changes have been made since the <a href="https://www.w3.org/TR/2018/WD-css-easing-1-20181009/">9 October
2018 Working Draft</a>:</p>
   <ul>
    <li data-md>
     <p>Reworded specification to refer to “easing functions”
rather than “timing functions”
and use more general language that does not assume these functions are only
applied to animations.</p>
   </ul>
   <h2 class="heading settled" data-level="5" id="acknowledgements"><span class="secno">5. </span><span class="content">Acknowledgements</span><a class="self-link" href="#acknowledgements"></a></h2>
   <p>This specification is based on the <a href="https://www.w3.org/TR/css3-transitions/">CSS Transitions</a> specification
edited by L.  David Baron, Dean Jackson, David Hyatt, and Chris Marrin.
The editors would also like to thank Douglas Stockwell, Steve Block, Tab Atkins,
Rachel Nabors, Martin Pitt, and the <a href="https://damp-lake-50659.herokuapp.com/">Animation at Work</a> slack
community for their feedback and contributions.</p>
  </main>
  <h2 class="no-ref no-num heading settled" id="conformance"><span class="content"> Conformance</span><a class="self-link" href="#conformance"></a></h2>
  <h3 class="heading settled" id="document-conventions"><span class="content"> Document conventions</span><a class="self-link" href="#document-conventions"></a></h3>
  <p>Conformance requirements are expressed with a combination of
	descriptive assertions and RFC 2119 terminology. The key words “MUST”,
	“MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”, “SHOULD NOT”,
	“RECOMMENDED”, “MAY”, and “OPTIONAL” in the normative parts of this
	document are to be interpreted as described in RFC 2119.
	However, for readability, these words do not appear in all uppercase
	letters in this specification. </p>
  <p>All of the text of this specification is normative except sections
	explicitly marked as non-normative, examples, and notes. <a data-link-type="biblio" href="#biblio-rfc2119">[RFC2119]</a> </p>
  <p>Examples in this specification are introduced with the words “for example”
	or are set apart from the normative text with <code>class="example"</code>,
	like this: </p>
  <div class="example" id="example-ae2b6bc0">
   <a class="self-link" href="#example-ae2b6bc0"></a> 
   <p>This is an example of an informative example. </p>
  </div>
  <p>Informative notes begin with the word “Note” and are set apart from the
	normative text with <code>class="note"</code>, like this: </p>
  <p class="note" role="note">Note, this is an informative note. </p>
  <p>Advisements are normative sections styled to evoke special attention and are
	set apart from other normative text with <code>&lt;strong class="advisement"></code>, like
	this: <strong class="advisement"> UAs MUST provide an accessible alternative. </strong> </p>
  <h3 class="heading settled" id="conform-classes"><span class="content"> Conformance classes</span><a class="self-link" href="#conform-classes"></a></h3>
  <p>Conformance to this specification
	is defined for three conformance classes: </p>
  <dl>
   <dt>style sheet 
   <dd>A <a href="http://www.w3.org/TR/CSS2/conform.html#style-sheet">CSS
			style sheet</a>. 
   <dt>renderer 
   <dd>A <a href="http://www.w3.org/TR/CSS2/conform.html#user-agent">UA</a> that interprets the semantics of a style sheet and renders
			documents that use them. 
   <dt>authoring tool 
   <dd>A <a href="http://www.w3.org/TR/CSS2/conform.html#user-agent">UA</a> that writes a style sheet. 
  </dl>
  <p>A style sheet is conformant to this specification
	if all of its statements that use syntax defined in this module are valid
	according to the generic CSS grammar and the individual grammars of each
	feature defined in this module. </p>
  <p>A renderer is conformant to this specification
	if, in addition to interpreting the style sheet as defined by the
	appropriate specifications, it supports all the features defined
	by this specification by parsing them correctly
	and rendering the document accordingly. However, the inability of a
	UA to correctly render a document due to limitations of the device
	does not make the UA non-conformant. (For example, a UA is not
	required to render color on a monochrome monitor.) </p>
  <p>An authoring tool is conformant to this specification
	if it writes style sheets that are syntactically correct according to the
	generic CSS grammar and the individual grammars of each feature in
	this module, and meet all other conformance requirements of style sheets
	as described in this module. </p>
  <h3 class="heading settled" id="conform-responsible"><span class="content"> Requirements for Responsible Implementation of CSS</span><a class="self-link" href="#conform-responsible"></a></h3>
  <p>The following sections define several conformance requirements
		for implementing CSS responsibly,
		in a way that promotes interoperability in the present and future. </p>
  <h4 class="heading settled" id="conform-partial"><span class="content"> Partial Implementations</span><a class="self-link" href="#conform-partial"></a></h4>
  <p>So that authors can exploit the forward-compatible parsing rules to assign fallback values, <strong>CSS renderers <em>must</em> treat as invalid
		(and <a href="http://www.w3.org/TR/CSS2/conform.html#ignore">ignore as appropriate</a>)
		any at-rules, properties, property values, keywords, and other syntactic constructs
		for which they have no usable level of support</strong>.
		In particular, user agents <em>must not</em> selectively ignore
		unsupported property values and honor supported values in a single multi-value property declaration:
		if any value is considered invalid (as unsupported values must be),
		CSS requires that the entire declaration be ignored. </p>
  <h4 class="heading settled" id="conform-future-proofing"><span class="content"> Implementations of Unstable and Proprietary Features</span><a class="self-link" href="#conform-future-proofing"></a></h4>
  <p>To avoid clashes with future stable CSS features,
		the CSSWG recommends <a href="http://www.w3.org/TR/CSS/#future-proofing">following best practices</a> for the implementation of <a href="http://www.w3.org/TR/CSS/#unstable">unstable</a> features and <a href="http://www.w3.org/TR/CSS/#proprietary-extension">proprietary extensions</a> to CSS. </p>
  <h4 class="heading settled" id="conform-testing"><span class="content"> Implementations of CR-level Features</span><a class="self-link" href="#conform-testing"></a></h4>
  <p>Once a specification reaches the Candidate Recommendation stage,
		implementers should release an <a data-link-type="dfn" href="http://www.w3.org/TR/CSS/#vendor-prefix">unprefixed</a> implementation
		of any CR-level feature they can demonstrate
		to be correctly implemented according to spec,
		and should avoid exposing a prefixed variant of that feature. </p>
  <p>To establish and maintain the interoperability of CSS across
		implementations, the CSS Working Group requests that non-experimental
		CSS renderers submit an implementation report (and, if necessary, the
		testcases used for that implementation report) to the W3C before
		releasing an unprefixed implementation of any CSS features. Testcases
		submitted to W3C are subject to review and correction by the CSS
		Working Group. </p>
  <p>
   Further information on submitting testcases and implementation reports
		can be found from on the CSS Working Group’s website at <a href="http://www.w3.org/Style/CSS/Test/">http://www.w3.org/Style/CSS/Test/</a>.
		Questions should be directed to the <a href="http://lists.w3.org/Archives/Public/public-css-testsuite">public-css-testsuite@w3.org</a> mailing list. 
<script src="https://www.w3.org/scripts/TR/2016/fixup.js"></script>
  </p>
  <h2 class="no-num no-ref heading settled" id="index"><span class="content">Index</span><a class="self-link" href="#index"></a></h2>
  <h3 class="no-num no-ref heading settled" id="index-defined-here"><span class="content">Terms defined by this specification</span><a class="self-link" href="#index-defined-here"></a></h3>
  <ul class="index">
   <li><a href="#before-flag">before flag</a><span>, in §2.3.1</span>
   <li><a href="#funcdef-cubic-bezier-easing-function-cubic-bezier">cubic-bezier()</a><span>, in §2.2</span>
   <li><a href="#typedef-cubic-bezier-easing-function">&lt;cubic-bezier-easing-function></a><span>, in §2.2</span>
   <li><a href="#cubic-bzier-easing-function">cubic Bézier easing function</a><span>, in §2.2</span>
   <li><a href="#valdef-cubic-bezier-easing-function-ease">ease</a><span>, in §2.2</span>
   <li><a href="#valdef-cubic-bezier-easing-function-ease-in">ease-in</a><span>, in §2.2</span>
   <li><a href="#valdef-cubic-bezier-easing-function-ease-in-out">ease-in-out</a><span>, in §2.2</span>
   <li><a href="#valdef-cubic-bezier-easing-function-ease-out">ease-out</a><span>, in §2.2</span>
   <li><a href="#easing-function">easing function</a><span>, in §2</span>
   <li><a href="#typedef-easing-function">&lt;easing-function></a><span>, in §2</span>
   <li><a href="#valdef-steps-end">end</a><span>, in §2.3</span>
   <li><a href="#input-progress-value">input progress value</a><span>, in §2</span>
   <li><a href="#valdef-steps-jump-both">jump-both</a><span>, in §2.3</span>
   <li><a href="#valdef-steps-jump-end">jump-end</a><span>, in §2.3</span>
   <li><a href="#valdef-steps-jump-none">jump-none</a><span>, in §2.3</span>
   <li><a href="#valdef-steps-jump-start">jump-start</a><span>, in §2.3</span>
   <li><a href="#valdef-easing-function-linear">linear</a><span>, in §2.1</span>
   <li><a href="#linear-easing-function">linear easing function</a><span>, in §2.1</span>
   <li><a href="#linear-easing-function">linear timing function</a><span>, in §2.1</span>
   <li><a href="#output-progress-value">output progress value</a><span>, in §2</span>
   <li><a href="#valdef-steps-start">start</a><span>, in §2.3</span>
   <li><a href="#typedef-step-easing-function">&lt;step-easing-function></a><span>, in §2.3</span>
   <li><a href="#step-easing-function">step easing function</a><span>, in §2.3</span>
   <li><a href="#valdef-step-easing-function-step-end">step-end</a><span>, in §2.3</span>
   <li><a href="#step-position">step position</a><span>, in §2.3</span>
   <li><a href="#typedef-step-position">&lt;step-position></a><span>, in §2.3</span>
   <li><a href="#funcdef-step-easing-function-steps">steps()</a><span>, in §2.3</span>
   <li><a href="#steps">steps</a><span>, in §2.3</span>
   <li><a href="#valdef-step-easing-function-step-start">step-start</a><span>, in §2.3</span>
   <li><a href="#easing-function">timing function</a><span>, in §2</span>
  </ul>
  <aside class="dfn-panel" data-for="term-for-comb-comma">
   <a href="https://drafts.csswg.org/css-values-4/#comb-comma">https://drafts.csswg.org/css-values-4/#comb-comma</a><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-comb-comma">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-comb-comma①">(2)</a> <a href="#ref-for-comb-comma②">(3)</a>
    <li><a href="#ref-for-comb-comma③">2.3. Step easing functions:
step-start, step-end, steps()</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="term-for-mult-opt">
   <a href="https://drafts.csswg.org/css-values-4/#mult-opt">https://drafts.csswg.org/css-values-4/#mult-opt</a><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-mult-opt">2.3. Step easing functions:
step-start, step-end, steps()</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="term-for-comb-one">
   <a href="https://drafts.csswg.org/css-values-4/#comb-one">https://drafts.csswg.org/css-values-4/#comb-one</a><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-comb-one">2. Easing functions</a> <a href="#ref-for-comb-one①">(2)</a>
    <li><a href="#ref-for-comb-one②">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-comb-one③">(2)</a> <a href="#ref-for-comb-one④">(3)</a> <a href="#ref-for-comb-one⑤">(4)</a>
    <li><a href="#ref-for-comb-one⑥">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-comb-one⑦">(2)</a> <a href="#ref-for-comb-one⑧">(3)</a> <a href="#ref-for-comb-one⑨">(4)</a> <a href="#ref-for-comb-one①⓪">(5)</a> <a href="#ref-for-comb-one①①">(6)</a> <a href="#ref-for-comb-one①②">(7)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="term-for-integer-value">
   <a href="https://drafts.csswg.org/css-values-3/#integer-value">https://drafts.csswg.org/css-values-3/#integer-value</a><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-integer-value">2.3. Step easing functions:
step-start, step-end, steps()</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="term-for-number-value">
   <a href="https://drafts.csswg.org/css-values-3/#number-value">https://drafts.csswg.org/css-values-3/#number-value</a><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-number-value">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-number-value①">(2)</a> <a href="#ref-for-number-value②">(3)</a> <a href="#ref-for-number-value③">(4)</a> <a href="#ref-for-number-value④">(5)</a> <a href="#ref-for-number-value⑤">(6)</a> <a href="#ref-for-number-value⑥">(7)</a> <a href="#ref-for-number-value⑦">(8)</a>
   </ul>
  </aside>
  <h3 class="no-num no-ref heading settled" id="index-defined-elsewhere"><span class="content">Terms defined by reference</span><a class="self-link" href="#index-defined-elsewhere"></a></h3>
  <ul class="index">
   <li>
    <a data-link-type="biblio">[css-values-4]</a> defines the following terms:
    <ul>
     <li><span class="dfn-paneled" id="term-for-comb-comma" style="color:initial">,</span>
     <li><span class="dfn-paneled" id="term-for-mult-opt" style="color:initial">?</span>
     <li><span class="dfn-paneled" id="term-for-comb-one" style="color:initial">|</span>
    </ul>
   <li>
    <a data-link-type="biblio">[CSS3VAL]</a> defines the following terms:
    <ul>
     <li><span class="dfn-paneled" id="term-for-integer-value" style="color:initial">&lt;integer></span>
     <li><span class="dfn-paneled" id="term-for-number-value" style="color:initial">&lt;number></span>
    </ul>
  </ul>
  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="normative"><span class="content">Normative References</span><a class="self-link" href="#normative"></a></h3>
  <dl>
   <dt id="biblio-css-values-4">[CSS-VALUES-4]
   <dd>Tab Atkins Jr.; Elika Etemad. <a href="https://www.w3.org/TR/css-values-4/">CSS Values and Units Module Level 4</a>. 31 January 2019. WD. URL: <a href="https://www.w3.org/TR/css-values-4/">https://www.w3.org/TR/css-values-4/</a>
   <dt id="biblio-css3val">[CSS3VAL]
   <dd>Tab Atkins Jr.; Elika Etemad. <a href="https://www.w3.org/TR/css-values-3/">CSS Values and Units Module Level 3</a>. 31 January 2019. CR. URL: <a href="https://www.w3.org/TR/css-values-3/">https://www.w3.org/TR/css-values-3/</a>
   <dt id="biblio-rfc2119">[RFC2119]
   <dd>S. Bradner. <a href="https://tools.ietf.org/html/rfc2119">Key words for use in RFCs to Indicate Requirement Levels</a>. March 1997. Best Current Practice. URL: <a href="https://tools.ietf.org/html/rfc2119">https://tools.ietf.org/html/rfc2119</a>
  </dl>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-cssom">[CSSOM]
   <dd>Simon Pieters; Glenn Adams. <a href="https://www.w3.org/TR/cssom-1/">CSS Object Model (CSSOM)</a>. 17 March 2016. WD. URL: <a href="https://www.w3.org/TR/cssom-1/">https://www.w3.org/TR/cssom-1/</a>
   <dt id="biblio-fund-comp-graphics">[FUND-COMP-GRAPHICS]
   <dd>Peter Shirley; Michael Ashikhmin; Steve Marschner. Fundamentals of Computer Graphics. 2009. 
  </dl>
  <aside class="dfn-panel" data-for="easing-function">
   <b><a href="#easing-function">#easing-function</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-easing-function">1. Introduction</a>
    <li><a href="#ref-for-easing-function①">2. Easing functions</a> <a href="#ref-for-easing-function②">(2)</a> <a href="#ref-for-easing-function③">(3)</a>
    <li><a href="#ref-for-easing-function④">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a>
    <li><a href="#ref-for-easing-function⑤">2.3. Step easing functions:
step-start, step-end, steps()</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="input-progress-value">
   <b><a href="#input-progress-value">#input-progress-value</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-input-progress-value">2. Easing functions</a> <a href="#ref-for-input-progress-value①">(2)</a>
    <li><a href="#ref-for-input-progress-value②">2.1. The linear easing function: linear</a>
    <li><a href="#ref-for-input-progress-value③">2.2.1. Output of a cubic bézier easing function</a> <a href="#ref-for-input-progress-value④">(2)</a> <a href="#ref-for-input-progress-value⑤">(3)</a> <a href="#ref-for-input-progress-value⑥">(4)</a> <a href="#ref-for-input-progress-value⑦">(5)</a> <a href="#ref-for-input-progress-value⑧">(6)</a>
    <li><a href="#ref-for-input-progress-value⑨">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-input-progress-value①⓪">(2)</a> <a href="#ref-for-input-progress-value①①">(3)</a> <a href="#ref-for-input-progress-value①②">(4)</a>
    <li><a href="#ref-for-input-progress-value①③">2.3.1. Output of
a step easing function</a> <a href="#ref-for-input-progress-value①④">(2)</a> <a href="#ref-for-input-progress-value①⑤">(3)</a> <a href="#ref-for-input-progress-value①⑥">(4)</a> <a href="#ref-for-input-progress-value①⑦">(5)</a> <a href="#ref-for-input-progress-value①⑧">(6)</a> <a href="#ref-for-input-progress-value①⑨">(7)</a> <a href="#ref-for-input-progress-value②⓪">(8)</a> <a href="#ref-for-input-progress-value②①">(9)</a> <a href="#ref-for-input-progress-value②②">(10)</a>
    <li><a href="#ref-for-input-progress-value②③">3. Privacy and Security Considerations</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="output-progress-value">
   <b><a href="#output-progress-value">#output-progress-value</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-output-progress-value">2. Easing functions</a> <a href="#ref-for-output-progress-value①">(2)</a>
    <li><a href="#ref-for-output-progress-value②">2.1. The linear easing function: linear</a>
    <li><a href="#ref-for-output-progress-value③">2.2.1. Output of a cubic bézier easing function</a> <a href="#ref-for-output-progress-value④">(2)</a> <a href="#ref-for-output-progress-value⑤">(3)</a>
    <li><a href="#ref-for-output-progress-value⑥">2.3.1. Output of
a step easing function</a> <a href="#ref-for-output-progress-value⑦">(2)</a> <a href="#ref-for-output-progress-value⑧">(3)</a> <a href="#ref-for-output-progress-value⑨">(4)</a> <a href="#ref-for-output-progress-value①⓪">(5)</a> <a href="#ref-for-output-progress-value①①">(6)</a>
    <li><a href="#ref-for-output-progress-value①②">3. Privacy and Security Considerations</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="linear-easing-function">
   <b><a href="#linear-easing-function">#linear-easing-function</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-linear-easing-function">2.1. The linear easing function: linear</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-easing-function-linear">
   <b><a href="#valdef-easing-function-linear">#valdef-easing-function-linear</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-easing-function-linear">2. Easing functions</a>
    <li><a href="#ref-for-valdef-easing-function-linear①">2.1. The linear easing function: linear</a>
    <li><a href="#ref-for-valdef-easing-function-linear②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="cubic-bzier-easing-function">
   <b><a href="#cubic-bzier-easing-function">#cubic-bzier-easing-function</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-cubic-bzier-easing-function">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-cubic-bzier-easing-function①">(2)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="typedef-cubic-bezier-easing-function">
   <b><a href="#typedef-cubic-bezier-easing-function">#typedef-cubic-bezier-easing-function</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-typedef-cubic-bezier-easing-function">2. Easing functions</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-cubic-bezier-easing-function-ease">
   <b><a href="#valdef-cubic-bezier-easing-function-ease">#valdef-cubic-bezier-easing-function-ease</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-valdef-cubic-bezier-easing-function-ease①">(2)</a>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-cubic-bezier-easing-function-ease-in">
   <b><a href="#valdef-cubic-bezier-easing-function-ease-in">#valdef-cubic-bezier-easing-function-ease-in</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease-in">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-valdef-cubic-bezier-easing-function-ease-in①">(2)</a>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease-in②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-cubic-bezier-easing-function-ease-out">
   <b><a href="#valdef-cubic-bezier-easing-function-ease-out">#valdef-cubic-bezier-easing-function-ease-out</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease-out">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-valdef-cubic-bezier-easing-function-ease-out①">(2)</a>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease-out②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-cubic-bezier-easing-function-ease-in-out">
   <b><a href="#valdef-cubic-bezier-easing-function-ease-in-out">#valdef-cubic-bezier-easing-function-ease-in-out</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease-in-out">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-valdef-cubic-bezier-easing-function-ease-in-out①">(2)</a>
    <li><a href="#ref-for-valdef-cubic-bezier-easing-function-ease-in-out②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="funcdef-cubic-bezier-easing-function-cubic-bezier">
   <b><a href="#funcdef-cubic-bezier-easing-function-cubic-bezier">#funcdef-cubic-bezier-easing-function-cubic-bezier</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-funcdef-cubic-bezier-easing-function-cubic-bezier">2.2. Cubic
Bézier easing functions:
ease, ease-in, ease-out, ease-in-out, cubic-bezier()</a> <a href="#ref-for-funcdef-cubic-bezier-easing-function-cubic-bezier①">(2)</a>
    <li><a href="#ref-for-funcdef-cubic-bezier-easing-function-cubic-bezier②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="step-easing-function">
   <b><a href="#step-easing-function">#step-easing-function</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-step-easing-function">2.3.1. Output of
a step easing function</a> <a href="#ref-for-step-easing-function①">(2)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="steps">
   <b><a href="#steps">#steps</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-steps">2.3.1. Output of
a step easing function</a> <a href="#ref-for-steps①">(2)</a> <a href="#ref-for-steps②">(3)</a> <a href="#ref-for-steps③">(4)</a> <a href="#ref-for-steps④">(5)</a> <a href="#ref-for-steps⑤">(6)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="step-position">
   <b><a href="#step-position">#step-position</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-step-position">2.3. Step easing functions:
step-start, step-end, steps()</a>
    <li><a href="#ref-for-step-position①">2.3.1. Output of
a step easing function</a> <a href="#ref-for-step-position②">(2)</a> <a href="#ref-for-step-position③">(3)</a> <a href="#ref-for-step-position④">(4)</a> <a href="#ref-for-step-position⑤">(5)</a> <a href="#ref-for-step-position⑥">(6)</a>
    <li><a href="#ref-for-step-position⑦">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="typedef-step-easing-function">
   <b><a href="#typedef-step-easing-function">#typedef-step-easing-function</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-typedef-step-easing-function">2. Easing functions</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="typedef-step-position">
   <b><a href="#typedef-step-position">#typedef-step-position</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-typedef-step-position">2.3. Step easing functions:
step-start, step-end, steps()</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-step-easing-function-step-start">
   <b><a href="#valdef-step-easing-function-step-start">#valdef-step-easing-function-step-start</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-step-easing-function-step-start">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-valdef-step-easing-function-step-start①">(2)</a>
    <li><a href="#ref-for-valdef-step-easing-function-step-start②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-step-easing-function-step-end">
   <b><a href="#valdef-step-easing-function-step-end">#valdef-step-easing-function-step-end</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-step-easing-function-step-end">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-valdef-step-easing-function-step-end①">(2)</a>
    <li><a href="#ref-for-valdef-step-easing-function-step-end②">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="funcdef-step-easing-function-steps">
   <b><a href="#funcdef-step-easing-function-steps">#funcdef-step-easing-function-steps</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-funcdef-step-easing-function-steps">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-funcdef-step-easing-function-steps①">(2)</a>
    <li><a href="#ref-for-funcdef-step-easing-function-steps②">2.4. Serialization</a> <a href="#ref-for-funcdef-step-easing-function-steps③">(2)</a> <a href="#ref-for-funcdef-step-easing-function-steps④">(3)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-steps-jump-start">
   <b><a href="#valdef-steps-jump-start">#valdef-steps-jump-start</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-steps-jump-start">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-valdef-steps-jump-start①">(2)</a>
    <li><a href="#ref-for-valdef-steps-jump-start②">2.3.1. Output of
a step easing function</a> <a href="#ref-for-valdef-steps-jump-start③">(2)</a> <a href="#ref-for-valdef-steps-jump-start④">(3)</a> <a href="#ref-for-valdef-steps-jump-start⑤">(4)</a> <a href="#ref-for-valdef-steps-jump-start⑥">(5)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-steps-jump-end">
   <b><a href="#valdef-steps-jump-end">#valdef-steps-jump-end</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-steps-jump-end">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-valdef-steps-jump-end①">(2)</a>
    <li><a href="#ref-for-valdef-steps-jump-end②">2.3.1. Output of
a step easing function</a> <a href="#ref-for-valdef-steps-jump-end③">(2)</a> <a href="#ref-for-valdef-steps-jump-end④">(3)</a>
    <li><a href="#ref-for-valdef-steps-jump-end⑤">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-steps-jump-none">
   <b><a href="#valdef-steps-jump-none">#valdef-steps-jump-none</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-steps-jump-none">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-valdef-steps-jump-none①">(2)</a>
    <li><a href="#ref-for-valdef-steps-jump-none②">2.3.1. Output of
a step easing function</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-steps-jump-both">
   <b><a href="#valdef-steps-jump-both">#valdef-steps-jump-both</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-steps-jump-both">2.3. Step easing functions:
step-start, step-end, steps()</a>
    <li><a href="#ref-for-valdef-steps-jump-both①">2.3.1. Output of
a step easing function</a> <a href="#ref-for-valdef-steps-jump-both②">(2)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-steps-start">
   <b><a href="#valdef-steps-start">#valdef-steps-start</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-steps-start">2.3. Step easing functions:
step-start, step-end, steps()</a>
    <li><a href="#ref-for-valdef-steps-start①">2.3.1. Output of
a step easing function</a> <a href="#ref-for-valdef-steps-start②">(2)</a> <a href="#ref-for-valdef-steps-start③">(3)</a> <a href="#ref-for-valdef-steps-start④">(4)</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="valdef-steps-end">
   <b><a href="#valdef-steps-end">#valdef-steps-end</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-valdef-steps-end">2.3. Step easing functions:
step-start, step-end, steps()</a> <a href="#ref-for-valdef-steps-end①">(2)</a>
    <li><a href="#ref-for-valdef-steps-end②">2.3.1. Output of
a step easing function</a> <a href="#ref-for-valdef-steps-end③">(2)</a>
    <li><a href="#ref-for-valdef-steps-end④">2.4. Serialization</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="before-flag">
   <b><a href="#before-flag">#before-flag</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-before-flag">2. Easing functions</a>
    <li><a href="#ref-for-before-flag①">2.3.1. Output of
a step easing function</a> <a href="#ref-for-before-flag②">(2)</a> <a href="#ref-for-before-flag③">(3)</a> <a href="#ref-for-before-flag④">(4)</a> <a href="#ref-for-before-flag⑤">(5)</a>
   </ul>
  </aside>
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